How can I create a circle that contains two existing vertices?
The difficulty here lies in the fact that it no longer seems to be a circular path, it seems to be elliptical and slanted.

Anyway you could probably achieve this easily by basic Extrude/Scale workflow using your already drawn profile as snapping guide.

Just select your last edge loop, press E to extrude, Z to restrict to the Z axis and then snap it to the first vertex of the guide.

To snap activate snapping to vertex in the 3d view header switch to Vertex Snap mode, and then press Ctrl during transform. 

Afterwards press S to scale Shift + Z to scale only in XY plane and then snap again to said vertex.

Repeat these steps until the complete shape is done.



In the end you may want to remove doubles to clean up the geometry by selecting all and pressing W > Remove Doubles